Many types of imaging techniques are known for deriving spatial information about a target object (or specimen). In conventional transmission imaging, an object is irradiated by plane wave illumination 10. The waves scattered by the object are re-interfered by a lens 12 to form an image, as shown in FIG. 1A. In the case of very short wavelength imaging (X-rays or electrons) this technique has many known difficulties associated with aberrations and instabilities introduced by the lens which limit the resolution and interpretability of the resulting image. Typical achievable resolution is many times larger than the theoretical wavelength limit. Conventional scanning transmission imaging is another example of such an imaging technique in which a lens is used to focus a spot of radiation through a target object. One or more detectors are located on the post target side of a target object to detect scattered radiation. Various types of detector strategies are known such as annular detectors, quadrant detectors and/or off-access detectors. However these methods rely on scanning the focused spot of radiation to all points where an image of the target object is required. There are a number of problems associated with such techniques such as the fact that very accurate control of the spot is required because if a 1000×1000 pixel image is desired a million accurate probe-position points must be used. Another problem is that the lens used must be of a very high quality. Not only is this because the resolution of the final, image is only as good as the sharpness and localisation of the spot but also because with various forms of radiation such as electrons or X-rays there are many problems such as aberration effects, chromatic spread and lens current instability which can affect image production and can ruin resolution. This is shown schematically in FIG. 1B in which incident radiation 15 such as an electron or X-ray beam is incident upon a specimen 16 which forms a target object. Radiation scattered by the object exits the target object and propagates onto detector plane 17.
Known problems with conventional scanning transmission imaging are that the images take a large time to complete due to the number of points which must be probed with the incident spot of radiation. If the target object moves during data collection this can lead to inaccurate data being collected and ultimately inaccurate images being produced. Also conventional scanning transmission imaging methods do not allow information relating to the phase of the radiation exiting the target object to be measured. Only total scattering intensity at the detectors can be measured. As such phase information relating to the exit wave that emanated beyond the target object cannot be gathered.
A modification of conventional scanning transmission imaging is four-dimensional de-convolution imaging. This utilises similar apparatus to that shown in FIG. 1 but records a whole diffraction pattern for every probe position. This provides a way of determining the structure of the target object at a better resolution than the spot size or response function of the lens used but has a number of major problems. The most notable problem is that huge quantities of data must be recorded which take hours to collect for a reasonable field of view. This makes the experiment practically very difficult to carry out because it is essential to control the probing illumination very accurately and to move it accurately to scan every (million) pixel for the final image reconstruction. Also severe damage to the target object can occur because huge doses of incident radiation are required for the large times taken.
Another well known imaging technique is pure diffractive imaging. In this alternative strategy the lens may be omitted and a target object is illuminated by a simple plane wave of probing radiation. The scattering pattern measured in the far field forms a Fourier plane diffraction pattern and the intensity of this may be recorded. An iterative method is then used by applying information derived from the intensity measured to calculate an estimated object exit wave field. In order to determine real information about the target object from the estimated wave field an area in real space must be provided where it is known that the object is absent or masked in some defined way. Only by knowing this fact can a running estimate of the wave field representing the object can be iteratively altered. There are however a multitude of problems associated with pure diffractive imaging. Most notably the target object must be suspended or isolated at some fixed location in some way. This is practically very difficult to achieve. Also it is not possible to extend the solution to new or different parts of the object or get a large image all at good resolution. Only one isolated region of an object can be illuminated and solved for. Also the target object must be single valued. That is, it must be represented by a single real number. That number may represent an absorption or a phase change but may not represent both. In fact most real target object waves (that is the wave function exiting a target object) appear as complex numbers having both phase and amplitude components.
Another major problem with pure diffractive imaging is that the edge of the target object must be sharply defined and thus have a distinct edge. This is so that an area where it is known that the object is absent or masked in some way is well defined. In practice it is difficult to produce an object or aperture having such a defined edge.
Further problems are that for weakly-scattering objects, which is a common type of target object in X-ray and electron scattering, most of the radiation passing through the object ends up at the centre of the diffraction pattern. Information in this zone is wasted as it does not aid in the image forming process but the radiation passing through the object can damage the object. Also parallel illumination is required. However this means that for a source of given brightness relatively few counts are provided at the object plane. In combination with the fact that much radiation passing through weakly-scattering objects terminates in a central zone as noted above this means that the whole experiment in practice takes a long time to get enough counts. If during the data collection stage the object or some other imaging apparatus drifts or moves during exposure data may be ruined.
A method for finding this solution which has gained considerable interest is the iterative method first suggested by Gerchberg and Saxton [R. W. Gerchberg and W. O. Saxton. Optik, 35(2): 237-246, 1972]. Such iterative methods have recently been applied to the geometry illustrated in FIG. 2 for both electrons and X-rays. In this arrangement incident radiation 20 is directed at a specimen 21 which forms a target object. The target object scatters the incident radiation in a wide angular range forming a diffraction pattern at a diffraction plane 22. The diffraction pattern in the diffraction plane 22 may be recorded via any suitable method such as a photographic film or CCD detector. The experimental advantage of diffraction is that the interference condition is determined only by scattering within the target object itself, and so the grave difficulties implied by using a short wavelength lens are avoided.